. Sketch the curves below WITHOUT using a graphing device!!!! (a) ~ r(t) = (cost,1 + cos2 t,0), 0 ≤ t ≤ π/2. (b) ~ r(t) = 4cost~ i +~ j + 4sint~ k, 0 ≤ t ≤ 2π 2. Determine ~ T(t) and ~ N(t) for the following curves. (a) ~ r(t) = (cost,2sint,1), 0 ≤ t ≤ 2π (b) ~ r(t) = (3sint,3cost,t), 0 ≤ t ≤ 2π 3. Determine the curvature for the following curves. (a) ~ r(t) = (cos3 t,2sin3 t,5), 0 ≤ t ≤ 2π (b) ~ r(t) = (4cost,sint,2cost), 0 ≤ t ≤ 2π
. Sketch the curves below WITHOUT using a graphing device!!!! (a) ~ r(t) = (cost,1 + cos2 t,0), 0...
3. (12 points) Consider the curve C defined by r(t) = (4 sint, -4 cost,0) with t€ (0,2) (a) Compute the length of the curve C. (b) Parametrize fit) with respect to are length measured from t = 0. (c) Determine the curvature of C.
3. (12 points) Consider the curve C defined by r(t) = (4 sint, -4 cost,0) with t € (0,2) (a) Compute the length of the curve C. (b) Parametrize f(t) with respect to arc length measured from t=0. (c) Determine the curvature of C.
(3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83, 2) with 0 2 t 1l F=(z-z, 0,2) r(t)-(cost, 0, sin t) with 0 t π F = (-y,2, 2) with r(t) = (-2 cost, 2 sin t, 2t) 0 < t < 2π
(3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83,...
(a) Sketch the curve r(t) = (e cost, e sint) in R2 and compute its are length for 0 < t < 87. For the sketch, use of software is acceptable, but the graph should be drawn by hand and the right features should be present.] (b) The vector v makes an angle of with the positive -axis. Write the vector v in component form. Furthermore, write the equation of the line lt') passing through the origin with direction vector...
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t
(1)...
1. The following questions involve the two polar curves: R 2+2sin20 and r 6sin 0 Sketch the curves and shade the region outside R and inside r. Use a large size graph paper and clearly indicate the points of intersection. Also indicate the values of theta that eive complete cycle for each curve. a b. Discuss the symmetry of each curve. ulate the area for the region of overlap that you shaded and described in part a. Show all steps...
An adiabatic steady-flow pumping device shown in the sketch
below employs a high pressure, high temperature stream of gas at
port 1 to pump a lower temperature stream of gas from a low
pressure at port 2 to a higher pressure at port 3. All of the gas
leaves the device at port 3 at the temperature T3. If the gas can
be modeled as an ideal gas with R = 2077 J/kg K and cP = 5234 J/kg
K,...
1. The following questions involve the two polar curves: R 2+2sin20 and r 6sin 6 Sketch the curves and shade the region outside R and inside r. Use a large size graph paper and clearly indicate the points of intersection. Also indicate the values of theta that give one complete cycle for each curve. Discuss the symmetry of each curve. a. b. Calculate the area for the region of overlap that you shaded and described in part a. Show all...
Hi need help for these Questions:
a. Given f = yi + xzk and g =
xyz2, determine (∇ x f ) .
∇g at the point (1,0,3)
b. Point A lies on the curve r(t) = 2 cos t i +
2 sin t j + t k for the range 0 ≤
t ≤ 2π . At point A, the tangent vector is T = -
21/2i +
21/2j + k. Determine
the co-ordinates of point A and...
Sign In d share 1. Plot the points (r, θ)-(3, π), ( 2år) , (1, π/4) and find the Eport PDA Create FDF Edit PDF rectangular (Cartesian) coordinates of the ponts without using a ca culator 2. Plot the point with rectangular coordinates (z, y)- and find the polar coordinates (r,0) for the point with r > 0 and 0 < θ < 2π without using a calculator. Then, find two other ways to write the point in polar coordinates....